Inverse Trigonometric Functions

32 solved questions from Class 12 Mathematics, each with the full working. Tap any question to see the step-by-step solution.

• 1 What is the domain, range, or fundamental theorem introduced in 'Inverse Trigonometric Functions' (Class 12 Mathematics)? medium MCQ Functions & Theorems
• 2 What is the derivative or integral formula associated with 'Inverse Trigonometric Functions'? medium MCQ Calculus & Formulae
• 3 How do you find the solution set or optimum value in 'Inverse Trigonometric Functions'? medium MCQ Problem Solving & Optimization
• 4 Find the domain of the function f(x)=tan^-1(√(1-x^2)). medium 2 marks Domain of composite inverse trig function
• 5 Solve for x (real) : sin^-1(2x)+cos^-1(x)=π/2. hard 5 marks Solving equations with inverse trig
• 6 Evaluate the definite integral ∫_0^(1/2) dx/√(1-4x^2). hard 4 marks Integration leading to inverse sine
• 7 Find the principal value of sin^-1(1/2). easy MCQ 1 mark Principal value of arcsin
• 8 Compute sin(2sin^-13/5). hard 4 marks Double‑angle formula with inverse sine
• 9 Find the principal value of tan^-1(-√3). easy MCQ 2 marks Principal value of inverse tangent
• 10 Solve for real x : tan^-1x + tan^-11/x=π/4. Mention any restrictions on x. hard 5 marks Sum of inverse tangents and principal values
• 11 Solve for x (real) : 2sin^-1x = π/3. medium 3 marks Solving equations with inverse sine
• 12 Solve for real x: tan^-1x - sin^-12x/(1+x^2) = 0. List all possible values of x. hard 5 marks solving equations with inverse trigonometric functions using substitution
• 13 Evaluate sin(3sin^-11/3).\n\n(a) 23/27\n(b) 7/9\n(c) 1/2\n(d) 5/27 medium MCQ 2 marks triple‑angle identity with inverse sine
• 14 Find the derivative dy/dx of y = sin^-1(2x/(1+x^2)) at x = 1. medium 2 marks differentiation of inverse sine composite function
• 15 Find the principal value of cos^-1(-√3/2). easy 1 mark principal value of inverse cosine
• 16 Solve for real x: tan^-1x + sin^-1(2x/(1+x^2))=π/2. State all possible solutions and any restrictions on x. hard 5 marks Solving equations involving inverse trig identities
• 17 Find the principal value of sin^-1(-1/2) in radians. easy MCQ 1 mark Principal value of inverse sine
• 18 Evaluate sin(2sin^-14/5). medium 2 marks Using double‑angle identity with inverse sine
• 19 Find dydx for y=cos^-1((1-x^2)/(1+x^2)) at x=1/√3. Give the numerical value. hard 4 marks Differentiation of inverse cosine using chain rule
• 20 Let y = sin^-1(2x/(1+x^2)) + cos^-1((1-x^2)/(1+x^2)). Find dy/dx and evaluate it at x=1/2. Give the final numerical value. hard 3 marks Derivative of a sum of inverse trig functions using identity
• 21 Find the principal value of sin^-1(-√2/2) in radians. medium 2 marks Principal value of inverse sine
• 22 Solve for real x: tan^-1(2x)=sin^-1(x). List all possible solutions. medium 2 marks Solving equations containing inverse trig functions
• 23 Evaluate cos(2cos^-15/13). easy MCQ 1 mark Double‑angle formula for cosine with inverse cosine
• 24 Find the principal value of cos^-1 (-1/2) in radians. easy 1 mark Principal value of inverse cosine
• 25 Solve for real x: sin^-1x + cos^-1(2x)=π/2. State all possible solutions and any restrictions on x. hard 4 marks Solving equation with inverse sine and cosine
• 26 Evaluate sin (2sin^-17/25). medium MCQ 2 marks Double‑angle using inverse sine
• 27 Let y=tan^-1 (2x/(1-x^2)). Find dydx and then evaluate it at x=1/2. hard 3 marks Derivative of composite inverse tangent
• 28 Evaluate displaystylesin(2sin^-1 3/5). easy MCQ 1 mark Double–angle for sine of arcsin
• 29 Find the principal value (in radians) of displaystylecos^-1!(-√3/2). medium 2 marks Principal value of arccos
• 30 Solve for real x: tan^-1x+tan^-1(2x)=π/4. State all solutions. hard 3 marks Equation with sum of arctangents
• 31 Let y=cos^-1!((1-x^2)/(1+x^2)). Find dydx and evaluate it at x=1/√3. Give the final numerical value. medium 2 marks Derivative of arccos with rational argument
• 32 Find the principal value (in radians) of displaystylesin^-1!(-3/5). medium 3 marks principal value of arcsine for negative arguments